***H: I have no idea what problem you are referring to. D: The problem of solving problems! Do you truly believe that problem is solved?***
Okay, write a step-by-step account using my 6AM scenario on once can came to face 'the problem of solving problems' and include in that account both the formulation of mathematics and its use in terms of solving 'the problem of solving problems'. I think if you do that you will see the futility in your question (which is why I suspect you won't do it).
***H: I don't even know why you think there is a problem unless you tell me step by step how you come to this 'problem'. D: Life is full of problems! Do you truly believe that no new problems will arise? If that is so, you must understand everything and I wish you would explain it to me.***
Dick, every problem known to man can be demonstrated to arise using this 6AM scenario. Your's is the only exception. You are basically admitting that you cannot explain how one can come to see this problem if they began life with just a self-aware sensation (i.e., no knowledge of the world). This indicates to me that this 'problem' is not a real problem since you cannot give this kind of account. Real problems can be shown step by step as to why they are real problems (versus pseudo-problems that arise from illogical steps taken in their formulation).
Here's an example of a pseudo-problem:
(1) Is natural selection the survival of the fittest?
(2) Then who are the fittest?
(C1) Answer: Those that survive! Circular reasoning.
(C2) Is natural selection the survival of those who survive?
The question in C2 is a pseudo-problem. It is constructed using invalid steps to construct a definition of natural selection which isn't quite correct (natural selection is a selection process of biological traits and not survivors per se). This is a formulated pseudo-problem that Creationists commonly use in their 'problem' for evolutionists. The 'problem' looks acceptable if you do not understand the intricacies of the question and the underlying assumptions of the question.
Similarly, your 'problem' is easily shown to be a pseudo-problem once we see the step-by-step reasoning that leads up to it. We see that there are invalid assumptions (i.e., logical fallacies) that are needed to construct the pseudo-problem. By keeping these steps hidden you are able to continue to say that it is a legitimate problem - even though it is not (e.g., "if I gave you my steps of inference that lead to my problem then you are violating the terms of my problem").
***H: Certainly you must use some inductive reasoning to realize there is a problem, right? D: Inductive reasoning? Sure! Mankind has solved problems in the past and I presume problems will be solved in the future! Does that seem like an irrational concept to you?***
Here's a case in point. You are being asked to give a sketch of how to formulate the problem as well the steps to making a solution, and you simply turn away from that proposal. The reason is that if you took this challenge your ill-founded assumptions would be quickly spotted and the game is over.
***H: On a napkin just write down what leads you to think there is a problem (step by step) and simply relay that to me. D: I just did!!***
No, a step-by-step account from knowing nothing other than having a self-aware sensation of the world. Surely, if you have a real problem you can construct that step-by-step account. Even the 'problem of solving problems' falls in that category.
***H: I guess we can't go any further here. D: Not if you are not interested in understanding what I did! As I said, there are only two paths which are rational to take! First, we could agree to disagree and forget this whole discourse which sure is the easy out. Or, I could show you what I propose to do and then, when I finish, and you understand what I have done you can decide for yourself if you think what I did was useful or not.***
Your whole formulation is based on a pseudo-problem (unless you can show otherwise this is my view). Every attempt I've made to understand your model always leads back to a misunderstanding of this pseudo-problem. If we cannot agree as to the correct formulation and soundness of this 'problem', then how can I know what you have accomplished. We don't agree on the very premise of your paper which I see as based on ill-founded assumptions. There's no more we can do. I think you need to formulate the problem and your attempted solution of this problem in a step by step account, and you don't think this is possible. Hence, I see the problem as a pseudo one. Using my analogy of the natural selection pseudo problem, as long as someone focused on that pseudo problem they will not be able to understand the solution that natural selection provides. There's no use in understanding natural selection as long as one insists that it is just a semantic tautological game.
***H: At first I thought there was one particular philosophical issue of science that you were trying to solve, but now I'm not so sure. D: You were the one who came up with the idea that I was trying to solve some philosophical issue! As far as I was concerned, I was solving a very particular problem. On the other hand, having solved that problem, I think personally that what I have found does indeed have some profound philosophical consequences. That is, my original path had nothing to do with solving any philosophical issues; however, knowing what I know now, my philosophical perspective is quite different than what it once was. But, if you canít understand what I propose, you certainly have no chance of even begining to comprehend the consequences of what I have discovered.***
Dick, this is all philosophy what you have proposed. The problem is philosophical (even though it is a pseudo problem). When you ask for about the problem of solving problems this is a philosophical dilemma. In addition, you have mentioned a number of philosophical reasons to need a solution (e.g., the faulty character of experiments to have terms defined that are true by definition, the fact that theories reference their own theoretical terms, the notion that deduction is more reliable means to proof than induction, etc).
***H: All I am sure of is that there is a problem that you have no idea why you know it and no idea why you are trying to solve it. D: The problem I propose to discuss is very simple. What can I do which will prepare me to answer a question in the future if I have no idea what that question will be?***
Okay, then show me step-by-step how that 'problem' arises as a dilemma to someone at 6AM who is just experiencing a self-aware sensation. I can demonstrate that this problem is a pseudo one by showing the assumptions inherent in it.
***You apparently stand steadfast behind the idea that "nothing of value can be done" and have no desire whatsoever to consider thinking otherwise! So, I guess blissful ignorance is itís own reward.***
Well, once you understand the pseudo-ness of this problem, then you will see why a correct formulation of this problem (known as Hume's problem of induction) isn't solved by your method and you will gain a much more deeper respect for the 3 centuries of effort gone into solving this problem of justifying the scientific approach to problems.
Warm regards, Harv